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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">E</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b4">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b3">F</font><br/>  for <font color="Olive" title="b5">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b4">TS</font>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Olive" title="b5">S</font>,<font color="Olive" title="b4">TS</font>) iff <font color="Olive" title="b5">S</font>,<font color="Olive" title="b2">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b4">TS</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> <br/>  for <font color="Olive" title="b2">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b3">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b2">F</font><br/>  for <font color="Olive" title="b4">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b3">TS</font>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Olive" title="b4">S</font>,<font color="Olive" title="b3">TS</font>) iff <font color="Olive" title="b4">S</font>,<font color="Olive" title="b1">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b3">TS</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span><br/>  for <font color="Olive" title="b2">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Olive" title="b1">F</font><br/>  for <font color="Olive" title="b3">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">TS</font>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b2">TS</font>) iff <font color="Olive" title="b3">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b2">TS</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">E</font> <a href="afinsq_1.html#K8" title="AFINSQ_1:func.8">^omega</a></span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">TS</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Maroon" title="c4">F</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">TS</font>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Olive" title="b2">S</font>,<font color="Olive" title="b1">TS</font>) iff <font color="Olive" title="b2">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Olive" title="b1">TS</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">TS</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rewrite3.html#L1" title="REWRITE3:struct.1">transition-system</a> over <font color="Maroon" title="c4">F</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">TS</font>  st  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/>( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Olive" title="b1">S</font>,<font color="Maroon" title="c5">TS</font>) iff <font color="Olive" title="b1">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">TS</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies ( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>) iff <font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:17"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>) iff <font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font> )</span><br/>

<span class="kw">thus </span><a NAME="E2:17"/>
( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>) implies <font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font> )
  <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font> implies <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>) )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:17_1"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font></span><br/>

<a NAME="E2:17_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c1">X</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="fsm_3.html#D1" target="_self" onmouseover="rs('fsm_3/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R1" title="REWRITE3:pred.1">--&gt;.</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#D2" onmouseover="rs('rewrite3/D2')" onmouseout="rh()">REWRITE3:def 2</a></span>;<br/>
<a NAME="E4:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c1">X</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T23" onmouseover="rs('rewrite3/T23')" onmouseout="rh()">REWRITE3:23</a></span>;<br/>
<a NAME="E5:17_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T87" onmouseover="rs('rewrite3/T87')" onmouseout="rh()">REWRITE3:87</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:17_1"/>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#D7" onmouseover="rs('rewrite3/D7')" onmouseout="rh()">REWRITE3:def 7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E3:17"/>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R4" title="REWRITE3:pred.4">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>)</span><br/>

<a NAME="E4:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R3" title="REWRITE3:pred.3">==&gt;*</a> <font color="Maroon" title="c1">X</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#D7" onmouseover="rs('rewrite3/D7')" onmouseout="rh()">REWRITE3:def 7</a></span>;<br/>
<a NAME="E5:17"/>
 ex <font color="Olive" title="b1">e</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">E</font> st <br/>( <font color="Maroon" title="c3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="flang_1.html#K3" title="FLANG_1:func.3">&lt;%</a><span class="default"><font color="Olive" title="b1">e</font></span><a href="flang_1.html#K3" title="FLANG_1:func.3">%&gt;</a></span> &amp; <font color="Maroon" title="c3">w</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">e</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="ref" href="fsm_3.html#T4" target="_self" onmouseover="rs('fsm_3/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<a NAME="E6:17"/><span class="kw">then </span>
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="rewrite3.html#R2" title="REWRITE3:pred.2">==&gt;.</a> <font color="Maroon" title="c1">X</font>, <a href="flang_1.html#K2" title="FLANG_1:func.2">&lt;%&gt;</a> <font color="Maroon" title="c2">E</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="ref" href="fsm_3.html#T12" target="_self" onmouseover="rs('fsm_3/T12')" onmouseout="rh()">Th12</a></span>;<br/>
<a NAME="E7:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font> <a href="rewrite3.html#R1" title="REWRITE3:pred.1">--&gt;.</a> <font color="Maroon" title="c1">X</font>, <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T24" onmouseover="rs('rewrite3/T24')" onmouseout="rh()">REWRITE3:24</a></span>;<br/>
<a NAME="E8:17"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite3.html#T15" onmouseover="rs('rewrite3/T15')" onmouseout="rh()">REWRITE3:15</a></span>;<br/>
<a NAME="E9:17"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font></span>)</span>
 
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">X9</font> = <font color="Maroon" title="c1">X</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">TS</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D1" target="_self" onmouseover="rs('fsm_3/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E11:17"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c3">w</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<font color="Maroon" title="c7">X9</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="rewrite3.html#U1" title="REWRITE3:sel.1">Tran</a> of <span class="p1">(<span class="default"><a href="fsm_3.html#K1" title="FSM_3:func.1">_bool</a> <font color="Maroon" title="c5">TS</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="ref" href="rewrite3.html#D2" onmouseover="rs('rewrite3/D2')" onmouseout="rh()">REWRITE3:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:17"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">w</font> <a href="rewrite3.html#K3" title="REWRITE3:func.3">-succ_of</a> (<font color="Maroon" title="c6">S</font>,<font color="Maroon" title="c5">TS</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="fsm_3.html#D1" target="_self" onmouseover="rs('fsm_3/D1')" onmouseout="rh()">Def1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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